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Differentiation of Exponential and Logarithmic Functions
Differentiation of Exponential and Logarithmic Functions
Exponential functions and their corresponding inverse functions, called logarithmic functions, have the following differentiation formulas:
Note that the exponential function f( x) = e x has the special property that its derivative is the function itself, f′( x) = e x= f( x). Example 1: Find f′( x) if
Example 2: Find
y′ if
.
Example 3: Find f′( x) if f( x) = 1n(sin x).
Example 4: Find
if
y=log
10(4
x 2 − 3
x −5).
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